The present invention relates generally to the field of fiber optic communications and specifically to the measurement of first- and higher-order polarization mode dispersion vectors in optical fibers.
Dispersion refers to the tendency of a light beam to spread out in time as it propagates through optical fiber. Several types of dispersion occur in optical fibers. One type is known as polarization mode dispersion.
Polarization mode dispersion refers to an effect that an optical device, such as a span of optical fiber, has on the separate polarizations of a light beam. A light beam can be approximated as having electrical components that vibrate at right angles to the direction of travel. In the simple case of a short fiber section the polarization or state of polarization of the light beam can be thought of as the direction of these right angle vibrations, where the light beam travels in a straight line. In the more general case, these components are superimposed in a more complex way. As shown in FIG. 1, within a short optical fiber section 10, an orthogonal set of two polarized waveguide modes 20 and 30 can be found which have electric field vectors aligned with the symmetry axes of the fiber. The polarization of a light beam propagating through the fiber section can be represented by vector components aligned with these polarization waveguide modes of the fiber as shown in FIG. 2. In FIG. 2, the polarization waveguide modes 20 and 30 are shown as two axes. The input polarization 40 is represented as the vector sum of two components 50 and 60 which are aligned with the polarization waveguide modes of the fiber section.
In ideal fiber, which has a perfect circular cross-section and is free from external stresses, the propagation properties of the two polarized waveguide modes are identical. However, imperfections introduced in the manufacturing process may result in fiber that is not perfectly circular. In addition, fiber that has been installed may suffer from external stresses such as pinching or bending. These manufacturing imperfections and external stresses cause the two polarized waveguide modes to have different propagation characteristics which in turn gives rise to polarization mode dispersion, or xe2x80x9cPMDxe2x80x9d.
PMD affects the polarization of a light beam with respect to both time and frequency. With respect to time, PMD causes the two vector components comprising the polarization of the light beam to propagate down the two polarization waveguide modes at different velocities and thus separate in time as seen in FIG. 3. In FIG. 3, the two components 50 and 60 of input polarization 40 are aligned with polarization waveguide modes 20 and 30. This time gap is known as the differential group delay, xe2x80x9cDGDxe2x80x9d or xcex94xcfx84. For the simple case of a short fiber section, PMD causes the polarization of the light beam at the output of the fiber section to vary with frequency in a periodic fashion when the polarization of the light beam at the input remains fixed. However, in the general case of PMD, most fibers can be modeled as many such fiber sections whose axes are oriented at random angles relative to each other. Although the behavior is more complex, the PMD effects of this random combination are similar to the simple case above over a narrow frequency range. Instead of two polarization waveguide modes, there are pairs of special polarizations, called the principal states of polarization, both at the input and output, displaying the differential group delay.
A convenient way to represent the effects of PMD caused by a particular optical device or span of optical fiber is using Stokes space, a three-dimensional geometrical space, and the Poincarxc3xa9 sphere, a sphere within Stokes space where every possible polarization state maps to a specific (and different) point on the sphere. For instance, the positive s1 axis of the Poincare sphere represents horizontal linear polarization, while the positive s2 axis represents 45-degree linear polarization, and all linear polarizations are on the equator.
The frequency effect of PMD can be easily seen when displayed on the Poincarxc3xa9 sphere. As shown in FIG. 4, for a light beam having a fixed input polarization 40, the output polarization 70 of the light beam moves locally in a circle on the surface of the Poincarxc3xa9 sphere as the frequency of the light beam is varied from xcfx891 to xcfx892 to xcfx893.
Using Stokes space and the Poincarxc3xa9 sphere, the various effects of PMD for a given optical device or span of fiber may be compactly represented using a single, three-dimensional vector referred to as the PMD vector or xcexa9. The magnitude of the PMD vector, |xcexa9|, describes the time effect of PMD and the rate of rotation of the output polarization with respect to frequency. In other words, |xcexa9|=xcex94xcfx84. The direction of the PMD vector describes the axis of the rotation. Finally, the direction of the PMD vector also describes an axis that intercepts the Poincarxc3xa9 sphere at two points on the surface of the sphere. These two intercept points represent the two principal states of polarization for the optical device or fiber.
A principal state of polarization, xe2x80x9cPSPxe2x80x9d, is a property of an optical device or span of fiber such that if a light beam""s polarization is aligned with the PSP at the input of the optical device or fiber, to first order, the light beam""s polarization at the output will not change when the light beam""s frequency at the input is varied. However, to second and higher orders with frequency, the output polarization does change. In the absence of polarization-dependent loss, each optical device or span of fiber has an orthogonal pair of PSP""s for each frequency. Polarization dependent loss refers to the difference in the amount of loss a light wave can experience with changes in its state of polarization.
Since PMD can limit the transmission bandwidth of optical fiber, measurement of the PMD of a span of fiber is necessary to determine the span""s data transmission capability as well as to provide information for compensating the PMD in the span. Although there are currently many methods for measuring PMD, most of these methods only provide a measurement of the magnitude of PMD, i.e., the differential group delay, and do not provide information on the PMD vector characteristics. Determination of the full vector characteristics of PMD is necessary for deducing the effects of higher order PMD. Higher order PMD describes the change of the PMD vector with frequency. Knowledge of the higher order PMD effects is necessary where there are significant changes of the PMD vector across the signal frequency bandwidth.
There are two commonly used methods that provide information on the PMD vectorxe2x80x94the Poincarxc3xa9 Sphere Technique, xe2x80x9cPST,xe2x80x9d and the Jones Matrix Eigenanalysis, xe2x80x9cJME.xe2x80x9d A general prior art apparatus for measuring PMD that is common to both methods is shown in block diagram form in FIG. 5. A light source 100 capable of operating at different frequencies, such as a tunable laser, inputs a light beam of a chosen frequency. A polarizing device 110, such as one or more linear polarizers, then imparts a chosen polarization state to the light beam. A control block 120, which could be a computer, controls the frequency of light source 100 and chooses the polarization imparted by polarizing device 110. The polarization state of the light beam may be represented by a vector in Stokes space and in the Poincarxc3xa9 sphere. The light beam then passes through the device under test 130 which could be a span of optical fiber. A measuring device 140, such as a polarimeter, measures the polarization state of the light beam at the output of the device under test. The data obtained from the measuring device is then analyzed in analysis block 150, which could be a computer, to determine the PMD vector characteristics.
The Poincarxc3xa9 Sphere Technique requires the input of at least two distinct polarization states, i.e. production of two light beams having distinct polarization states. For each input polarization state, the input frequency is varied and the output polarization state measured. The resulting data is then differentiated with respect to frequency to obtain the magnitude and direction of the PMD vector.
The Poincarxc3xa9 Sphere Technique has several shortcomings. First, although the input of two distinct polarization states is required, the input of a third distinct polarization state is often necessary. Where the resulting PMD vector would be coplanar with the vectors representing the first two polarization states in Stokes space, subsequent calculations using data only from these first two polarization states would be impossible because there would be division by zero. In such an instance, additional data must be obtained from the input of a third distinct polarization state. This input of an additional polarization state adds complexity to the overall testing system because a circular or elliptical polarizer must be used to input this third polarization state whereas linear polarizers are sufficient for the first two input polarization states.
Another shortcoming of the Poincarxc3xa9 Sphere Technique is that for each input polarization state, measurements must be taken at closely spaced frequencies. In practicality, it is very difficult to obtain accurate data for small frequency intervals using currently available commercial instrumentation. Such data often suffers from a low signal-to-noise ratio.
The Jones Matrix Eigenanalysis inputs three input polarization states at a first frequency and then measures the corresponding output polarization states. From the known input polarization states and the measured output polarization states, the Jones matrix corresponding to the first frequency is calculated. The process is repeated for a second frequency and from the two Jones matrices, the PMD vector may be calculated. Thus a total of six light beams must be input to the optical device under test.
The JME method does not necessarily suffer from data with a low signal-to-noise ratio because in the JME method, measurements can be taken at larger frequency intervals. However, using larger frequency intervals over the same frequency range results in the problem of fewer measurements being taken and thus fewer data points being available. In turn, fewer data points reduces the resolution of a plot of the changes of PMD with frequency. Without adequate resolution of the plot of first order PMD, determinations of higher orders of PMD become inaccurate.
The JME method also has other shortcomings. Although the initial measurements of the output polarizations are done in Stokes space, the data is then converted to Jones space in order to obtain the Jones matrices. The results from the Jones matrices must then be reconverted to Stokes space in order to obtain the PMD vector. In addition to these added conversion and reconversion steps, the calculations themselves which are done in Jones space are more complicated than calculations performed within Stokes space. Thus, the algorithm to calculate the PMD vector with this method is much more complex than an algorithm which calculates the PMD vector fully within Stokes space.
Another shortcoming of the JME method is that the relative angles between the first, second, and third input polarization states must be known precisely in order to perform the calculations of the JME method. In practice, it is difficult to precisely determine the relative angle between the input polarization states. Consequently, accuracy in the subsequent PMD calculations may suffer.
The present invention consists of a method and apparatus for measuring first and higher order PMD vectors in optical fibers. Unlike existing methods, the current method requires the input of only two distinct polarization states. Also, the method of the present invention does not require knowledge of the relative angle between the two polarization states. In addition, the algorithm of the present method is simpler than that of the prior art because it remains entirely in Stokes space. The frequency interval of each measurement pair can be large to enable a high signal-to-noise-ratio measurement of each individual PMD vector. Finally, the frequency interval between each individual PMD vector determination (i.e. at the center frequency of each pair) can be small, providing good resolution of PMD variation with frequency. This allows accurate determination of second-order PMD.
For each PMD vector to be determined, four light beams are sequentially injected into an optical device under test, or xe2x80x9cDUTxe2x80x9d, the first light beam having a frequency xcfx89 and a first polarization state represented by vector s1 in Stokes space, the second light beam having a frequency xcfx89 and a second polarization state represented by vector sa in Stokes space, the third light beam having a frequency xcfx89+xcex94xcfx89f and a first polarization state represented by vector s1 in Stokes space, and the fourth light beam having a frequency xcfx89+xcex94xcfx89f and a second polarization state represented by vector sa in Stokes space. In other words, two distinct polarization states, represented by Stokes vectors s1 and sa, are sequentially injected into an optical device under test with each polarization state being injected at a pair of frequencies xcfx89 and xcfx89+xcex94xcfx89f. Of the four numbers needed to fully describe s1 and sa, only three are needed by the algorithm. This provides experimental simplicity. For instance, linear polarizers can be used to provide s1 and sa, but the angle between them need not be known.
Note that vector s1 must not be parallel or anti-parallel to vector sa. Also, the frequency interval xcex94xcfx89f is large but should not exceed xcfx80/xcex94xcfx84m, where xcex94xcfx84m is the peak PMD of said DUT in the frequency span measured. Better accuracy can be obtained with large xcex94xcfx89f.
The polarization state of the four light beams coming out of the optical device under test are measured, and four output Stokes vectors representing each measured polarization state in Stokes space are determined. A first-order PMD vector is then determined from the four input Stokes vectors, i.e., s1 at xcfx89 and xcfx89+xcex94xcfx89f and sa at xcfx89 and xcfx89+xcex94xcfx89f, and from the four output Stokes vectors. Each subsequent PMD vector determination is then made using a pair of frequencies which is greater than the previous pair of frequencies by a frequency interval xcex94xcfx89i which is small compared to xcex94xcfx89f. Thus, if xcfx890 and xcfx890+xcex94xcfx89f is the first pair of frequencies used, then xcfx891 and xcfx891+xcex94xcfx89f is the second pair of frequencies used, and xcfx892 and xcfx892+xcex94xcfx89f is the third pair of frequencies used, etc., where xcfx891=xcfx890+xcex94xcfx89i, and xcfx892=xcfx891+xcex94xcfx89i, etc., and xcex94xcfx89i less than xcex94xcfx89f. This technique of using a smaller frequency interval between each pair than the frequency interval separating the frequencies of each pair can be used with any PMD measurement method to provide good resoultion of PMD variation with frequency. It will be recognized by one skilled in the art that the intervals xcex94xcfx89f and xcex94xcfx89i can vary for different pairs.